PROPERTIES OF curl(phi) AND grad(phi)+curl(phi) CLASSES OF SOLUTION TO THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

The solution in the special classes of curl(phi) and gard(phi)+curl(phi) of Navier-Stokes equations is investigated in this work. Analysis is taken using the vorticity equations rather than the original Navier Stokes equations based on the work of Chae and Choe [1]. Derivations show that the corresponding problem can be transformed to the class of linear parabolic and elliptic equations. Analysis is performed on L-infinite,L-2 and L-p theory of solutions to linear problems. Results show that the corresponding problems admit unique and regular solutions.